Robert Alexander Allardyce's father?

I have psitively identified my grandparents in Iowa during the 1880/90s. My grandmother, Laura Horner Allardyce then moved to Minneapolis with most of my aunts and uncles - one of which was Fred and another James Allardyce. I'm trying to find a solid link with my great grandfather Allardyce - probably in London for at least some of his life (1870s) I think William Lamond Allardyce is related as my aunt Muriel left me a couple of news clippings about him. I doubt she would have kept them had they not been relevant. Thanks,